I have an island light that I will use as a swag, don't want to put in new junction box. I have the swag kit, but what do I do with the ground wire that is installed on the light?

I don't quite understand. Where you connect the light to the house wiring, you must have a box. Is there an existing ceiling fixture you want to convert to a swag light?

If you plan to terminate the two insulated line wires with a male plug, you need to use a three wire plug.

If you connect the wires to a box at the end of the chain, use an approved connector or bushing into a blank cover. Splice the ribbed line wire to the white, the smooth line wire to the black or which ever wire is controlled by a switch, and the bare stranded ground wire from the lamp to the bare or green wire, or connect to the metal box, providing it is grounded.
If this is not helpful , get back with more detail of your situation.